# Correlation Coefficient, Hypothesis Testing with Confidence Interval

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1. The manager of a movie rental store was interested in examining the relationship between the weekly take-home pay for a family and the amount that family spends weekly on recreational activites. The following output was generated using Minitab:

Covariances

takehome recreation

takehome 4413.84

recreation 2419.64 1364.29

Let 2=weekly take-home pay and y=amount spent weekly on recreational activities

a. identify s of x squared (=4413.84)

b. s of xy (=1364.29)

c. s of y squared (=2419.64)

d. calculate the correlation between weekly take-home pay and amount spent weekly on recreational activities.

e. Interpret the correlation coefficient found in part d.

2. Furnish 2 offices each with a desk, chair and file cabinet and 2 bookcases. At a local store there are 6 models of desks, 8 models of chairs, 4 models of file cabinets and 10 models of bookcases. How many choices do you have if you want to select two desks, two chairs, two file cabinets and four bookcases if you dont want to select more than one of any model?

3. Determine whether the average number of calories in a homemade cookie is more than a store-bought one. Estimate the difference in the mean calories between the two types using a 90% confidence interval.

homemade n=40 x-bar=180 s=2

storebought n=45 x-bar=179 s=4

4. A childcare agency was interest in examining the amount that families pay per child per month for childcare outside the home. A random sample of 64 families was selected and the mean and the standard deviation were computed to be $675 and $80 respectively.

a. Find a 95% confidence interval for the true average amount spent per child per month for childcare outside the home.

b. Interpret the interval found in part a.

c. A social worker claims that the average amount spent per child per month outside the home is $700. Based on the interval in part a can this claim be rejected?

d. Find a 95% upper confidence bound for the true average amount spent per child per month on childcare outside the home.

5. In the past it took Kim 148.4 seconds to swim 200 meters. Kim wants to know if her average has changed. She records her time on 50 randomly selected occasions and computes the mean to be 147.8 seconds with a standard deviation of 2.3 seconds.

a. Perform the appropriate test of hypothesis to determine whether Kim's average time has changed. Use alpha=.01.

b. Compute the power of the test if Kim's actual mean swimming time is 147.3 seconds. Interpret the results.

6. A student representative claims that 60% of the students favor a move to division 1. A random sample of 250 students were selected and 140 of them indicated they favored a move to division 1.

a. Perform the appropriate test of hypothesis to test the representative's claim. Use alpha=.05.

b. Write out each step in determining the p-value for the test in part one.

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##### Solution Summary

1. The manager of a movie rental store was interested in examining the relationship between the weekly take-home pay for a family and the amount that family spends weekly on recreational activites. The following output was generated using Minitab:

Covariances

takehome recreation

takehome 4413.84

recreation 2419.64 1364.29

Let 2=weekly take-home pay and y=amount spent weekly on recreational activities

a. identify s of x squared (=4413.84)

b. s of xy (=1364.29)

c. s of y squared (=2419.64)

d. calculate the correlation between weekly take-home pay and amount spent weekly on recreational activities.

e. Interpret the correlation coefficient found in part d.

2. Furnish 2 offices each with a desk, chair and file cabinet and 2 bookcases. At a local store there are 6 models of desks, 8 models of chairs, 4 models of file cabinets and 10 models of bookcases. How many choices do you have if you want to select two desks, two chairs, two file cabinets and four bookcases if you dont want to select more than one of any model?

3. Determine whether the average number of calories in a homemade cookie is more than a store-bought one. Estimate the difference in the mean calories between the two types using a 90% confidence interval.

homemade n=40 x-bar=180 s=2

storebought n=45 x-bar=179 s=4

4. A childcare agency was interest in examining the amount that families pay per child per month for childcare outside the home. A random sample of 64 families was selected and the mean and the standard deviation were computed to be $675 and $80 respectively.

a. Find a 95% confidence interval for the true average amount spent per child per month for childcare outside the home.

b. Interpret the interval found in part a.

c. A social worker claims that the average amount spent per child per month outside the home is $700. Based on the interval in part a can this claim be rejected?

d. Find a 95% upper confidence bound for the true average amount spent per child per month on childcare outside the home.

5. In the past it took Kim 148.4 seconds to swim 200 meters. Kim wants to know if her average has changed. She records her time on 50 randomly selected occasions and computes the mean to be 147.8 seconds with a standard deviation of 2.3 seconds.

a. Perform the appropriate test of hypothesis to determine whether Kim's average time has changed. Use alpha=.01.

b. Compute the power of the test if Kim's actual mean swimming time is 147.3 seconds. Interpret the results.

6. A student representative claims that 60% of the students favor a move to division 1. A random sample of 250 students were selected and 140 of them indicated they favored a move to division 1.

a. Perform the appropriate test of hypothesis to test the representative's claim. Use alpha=.05.

b. Write out each step in determining the p-value for the test in part one.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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